Poisson regression and Zero-inflated Poisson regression: application to private health insurance data

Modeling event counts is important in many fields. For this purpose, the Poisson regression model is often used. However, this model assumes the equidispersion of the data. Unfortunately, this assumption is often violated in the observed data. The source of overdispersion depends on many situations. When the source of overdispersion is the excess of zeroes, the Zero-inflated Poisson regression model fits better counts data. In this paper, we first review the theoretical framework of Poisson regression and Zero-inflated Poisson regression. The probability integral transform test and the Vuong's test are used to compare between the two models. Second, we fit these models to the number of claims in a private health insurance scheme. In our case, the number of claims is overdispersed because of the preponderance of zeroes in the data set. The results prove that Zero-inflated Poisson regression performs better the number of claims of the customers affiliated in the health insurance scheme in the Moroccan case.